On lacunary Toeplitz determinants

Abstract

By using Riemann–Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants det _N[c_ℓa−mb[f]] generated by holomorphic symbols, where ℓ_a=a (resp. m_b=b) except for a finite subset of indices a=h₁,…,h_n (resp. b=t₁,…,t_r). In addition to the usual Szegö asymptotics, our answer involves a determinant of size n+r.